Show that 7 ° is about 1 50 of the circumference of a circle

The circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle as if it were opened up and straightened out to a line segment. If a point took around a point mass, then its path length is a circle. It has to move about 2 π radiam = 360 ° around the centre to complete a circumference, therefore we have, 360 ° = 1 circumference Therefore 7 ° = 7 360 ≃ 1 50 circumference

Eratosthenes calculated that the distance between Syene and Alexandria, 5000 stadia represented the same fraction, 1 50 of the Earth's circumference. Use your answer above to calculate Eratosthenes's circumference of the Earth (giving your answer in stadia).

Given that the distance measured by Eratosthenes between Syene and Alexandria is 5000 stadia It is the 1 50 fraction ( 7 ° a r c ) of the total circumference of the earth, Therefore, the circumference of the Earth as measured by him is 5000 × 50 = 250000 stadia .

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MYP Physics A concept-based approach Years 4&5>Chapter 7 - Form>Measuring the circumference of the Earth

William Heathcote Solutions for Chapter: Form, Exercise 3: Measuring the circumference of the Earth

Author:William Heathcote

William Heathcote Physics Solutions for Exercise - William Heathcote Solutions for Chapter: Form, Exercise 3: Measuring the circumference of the Earth

Attempt the practice questions on Chapter 7: Form, Exercise 3: Measuring the circumference of the Earth with hints and solutions to strengthen your understanding. MYP Physics A concept-based approach Years 4&5 solutions are prepared by Experienced Embibe Experts.

Questions from William Heathcote Solutions for Chapter: Form, Exercise 3: Measuring the circumference of the Earth with Hints & Solutions

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MYP:4-5

IMPORTANT

MYP Physics A concept-based approach Years 4&5>Chapter 7 - Form>Measuring the circumference of the Earth>Q 1

Show that $7 °$ is about $\frac{1}{50}$ of the circumference of a circle

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MYP:4-5

IMPORTANT

MYP Physics A concept-based approach Years 4&5>Chapter 7 - Form>Measuring the circumference of the Earth>Q 2

Question Image

Eratosthenes calculated that the distance between Syene and Alexandria, $5000 stadia$ represented the same fraction, $\frac{1}{50}$ of the Earth's circumference. Use your answer above to calculate Eratosthenes's circumference of the Earth (giving your answer in stadia).

MEDIUM

MYP:4-5

IMPORTANT

MYP Physics A concept-based approach Years 4&5>Chapter 7 - Form>Measuring the circumference of the Earth>Q 3

Question Image

Eratosthenes calculated that the distance between Syene and Alexandria, $5000 stadia$ represented the same fraction, $\frac{1}{50}$ of the Earth's circumference. Use your answer above to calculate Eratosthenes's circumference of the Earth (giving your answer in stadia).

If one stade is $160 m$ calculate the circumference of the Earth in meters.

MEDIUM

MYP:4-5

IMPORTANT

MYP Physics A concept-based approach Years 4&5>Chapter 7 - Form>Measuring the circumference of the Earth>Q 4

Question Image

Eratosthenes calculated that the distance between Syene and Alexandria, $5000 stadia$ represented the same fraction, $\frac{1}{50}$ of the Earth's circumference. Use your answer above to calculate Eratosthenes's circumference of the Earth (giving your answer in stadia).

If one stade is $160 m$ calculate the circumference of the Earth in meters. Compare this answer to the value that is currently accepted.